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Unformatted text preview: 1 Theory of Solids HW-11 Solution By Qifeng Shan Ashcroft and Mermins book 13-2 Deduce from (13.25) that at T = 0 (and hence to an excellent approximation at any T << T F ) the conductivity of a band with cubic symmetry is given by , 12 3 2 S v e F (13.71) where S is the area of Fermi surface in the band, and v is the electronic speed averaged over the Fermi surface: . ) ( 1 k v dS S v (13.72) (Note that this contains, as a special case, the fact that filled or empty bands (neither of which have any Fermi surface) carry no current. It also provides an alternative way of viewing the fact that almost empty (few electrons) and almost filled (few holes) bands have low conductivity, since they will have very small amounts of Fermi surface.) Verify that (13.71) reduces to the Drude result in the free electron limit. Solution: From Eq. (13.25): ....
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